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z=plk, Yj=B!A-0 •

(88')

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0TMeTHM eru.e, lJTO IIpH p<k, KaK BHJI.HO H3 cpaBHeHHH <t>opMyJI (83)

H (86), <Pa3bl BbiHYlliJI.eHHb!X KOJie6amiH ll B03MYIII.aiOIII.eH CHJibl BCe BpeMH COBIIaJI.aiOT ( o6e paBHbi pf). ECJIH llie p>k, TO, BHOCH MHHYC IIO)l, 3HaK CHHyca, MOlliHO rrpeJI.CTaBHTb ypaBHeHHe (86) B BHJI.e

X2= 2Pok2 sin(pt-:rt). p -

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HO B03paCTaTb TaK, KaK 3TO IIOKa3aHO Ha
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ca) paCCMOTpeHbl B KOHUe 3T0f0 naparpa<t>a
(rr. 3).
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= Bsinpt He nMeeT, n no pernerme 6y,n:eM ncKaTb B Bn,n:e	Pnc.	262
	Pnc.	262

x2= Ct cos pt.

Tor,n:a x2=-2Cpsinpf-p2Ctcospt, ll llO;J:CT3HOBKa B ypaBHeHHe (85), CCJIH y'!eCTb,'!TO p=k, ,n:aeT -2Cpsinpt=P0 sinpt, OTKy,n:a C=-P0 12p. B pesym..TaTe naxo,n:HM saKOH

Bb!Hy:lKJ(eHHblX KOJie6aHHH npn pe30HaHCe B CJiyqae OTCyTCTBllH COI!pOTHBJieHHH:

x 2= - (P012p)tcospt HJIH x2= (P0/2p)tsin (pt-n/2),

(89)

243

JvtUtiecKoii cKOpocmbiO

CKopocTh V1 =VgR,

§ 98. HCKYCCTBEHHbiE CUYTHHKH 3EMJIH.

3JIJIHOTHIIECKHE TPAEKTOPHH

TipH Vo<V2gR H a=/=rc/2 TpaeKTOpHH TeJia, 6porueHHOrO c se:vmofi noBepxnocTH, eCTh 3JIJIHnc, y KOTOporo och PA, o6pasy10maH c Ox

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rrepeceqeT nOBepXHOCTb	3eMJIH	B CHMMeTpH4HOH OTHOCHTeJihHO OCH
PA T04Ke M 1 , T. e. TeJio	yrra)l,eT	Ha 3eMJIIO. CJie)l,oBaTeJihHO, 6powen-

Hoe TeJIO MOllieT CTaTh cnyTHHKOM 3eMJIH JIHillh npH TeX HaqaJihHbiX yc-

JIOBHHX, KOTOpbie )l,a!OT ~ =rc. Ho, KaK nOKa3biBaiOT paBeHCTBa (111), ~=rc TOJihKO npn a=O (HJIH a=rc) H v~~gR, TaK KaK npn P=rc H

v~<gR nepBOe H3 paBeHCTB (111) )l,aeT e<O, 4TO HeB03MOlliHO, nOCKOJih· r<y e - BeJIH4HHa rroJIOlliHTeJihHaH. CJie)l,OBaTeJihHO, 4T06hr TeJio, 6po-

rneHHOe C 3eMHOH nOBepXHOCTH, npeBpaTHJIOCh B cnyTHHKa 3eMJIH, Heo6xo)l,HMO BbiiiOJIHeHne )l,Byx ycJIOBHli:

a=O, V2goRo>Vo~VgoRo·

(114)

3KCUeHTpHCHCTeT Op6HTbl cnyTHHKa npH a=Q H P=rc, KaK BH)l,HO H3 paBeHCTB (111) HJIH (113), 6y)l,eT

(115)

npn KOTopofi e=O n cnyTHIIK )l.BHllieTCH no KpyroBofi op6nTe pa)l.nyca R, Ha3biBaeTCH Kpyzoeoa HJIH nepeou KOc- [eM.§ 82, ¢opMyJia (28)]. Tipn 6pocannn c rroBepxHOCTH 3eMJIH, ecJIH C4HTaTb R=R 0 =6378 KM H g=g0 =9,82 M/c2 , rrep-

BaH KOCMH4eCKa5I CKOpOCTb Vl~7,9 KM/C. TipH Vo>V1 Op6HTOH cnyTHHKa 6y)l,eT 3JIJIHnC, 3KCUeHTpHCHTeT KOTOpOrO TeM 60Jrhrne, 4eM 60Jihille

V0 (pnc. 270).

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CKOtl CKOpOCffib/0,

254

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MOJKHbiM IIOJiytreHHe CIIYTHHKOBOrO )l:BHJKeHHH H npH	~=:fo0. 0)l:HaKO
HeTPYAHO ITO)l:CtrHTaTb, trTO rrpH yseJIHtreHHH H (XOTH V1 ,	HarrpHMep, ITPH

3TOM yMeHblliaeTCH) IIOJ!HaH 3HeprHH, 3aTpatrHBaeMa5I Ha 3aiiyCK CrryT-

HHKa )l:aHHOH MaCChi, B03paCTaeT.

9JIJIIIITTHtreCKHe TpaeKTOpHH. Tipn~>O H V 0 <Vr2g0 R0

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6aJIJII1CTwrecKne paKerhr, B traCTHOCTH MemKoHTHHeHTaJibHbie. Haii:)l:eM OCHOBHble xapaKTepHCTHKH 3THX TpaeKTOpHH.

TaK KaK ocb PA HBJIHeTCH och!O CHMMeTpHII TpaeKTopnn, TO TOtrKOH

na)l:eHHH 6y)l:eT M1 H )l:aJibHOCTb S 6y)l:eT paBHa )l:JIIIHe AYrii M--:;M1 (eM.

'pnc.269);	CJie)l:OBaTeJibHO,								(116)
				S=2Ro~.
f)l:e ~ OITpe)l:eJIHeTCH cpopMyJIOH (112). TipH 3TOM,									KaK 06bltrHO ITpHHHTO,
B paBeHCTBe (116) Ro- cpe)l:HIIH pa)l:nyc 3eMJIH.
Han6oJihWaH		BbiCOTa		H	TpaeKTopnn paBHa (r)IJl=fl -Ro IIJIH,
COfJiaCHO	paBeHCTBaM		(109)	II	(110),			-R
			H _		2	2	a
					vo cos				(117)
				-	(1-e) go			o•

r)l:e e onpe)l:eJIHeTCH cpopMyJioii: (113).
BpeMH	ITOJieTa	T	Haii:)l:eM		H3	ypaBHeHHH			(103), KOTOpoe BMecTe
c (104) )l:aeT		dt= (r 2/c) dcp= (r 2IR 0V 0 cos~) dcp.